But he added the government could have done more for Mr Henning in captivity, "when they knew about it, months and months ago".

'Absolutely abhorrent'

The prime minister described Mr Henning as a "kind, gentle, compassionate and caring man".

Speaking at Chequers following a briefing from defence and intelligence officials, including the head of MI5, Mr Cameron said the murder was "absolutely abhorrent".

"It is senseless, it is completely unforgiveable," he added.

"Anyone in any doubt about this organisation can now see how truly repulsive and barbaric it is.

"And as a country, what we must do, with our allies, is everything we can to defeat this organisation in the region, but also to defeat it at home, and we must do everything we can to hunt down and find the people who are responsible for this."

Alan Henning was on his fourth aid mission to Syria

IS had threatened to kill Mr Henning in video footage last month showing the death of Briton David Haines.

In the most recent video, the extremist group threatens US aid worker Peter Kassig.

BBC security correspondent Gordon Corera said the footage was similar to previous videos released by IS and included a reference to last week's vote by Parliament to authorise air strikes against IS in Iraq.

Like previous videos it features a militant who, from his accent, appears to be from Britain.

Mr Cameron said "all the assets" the government has would be used to try to find and help remaining hostages.

He added the government would "do everything we can to defeat this organisation which is utterly ruthless, senseless and barbaric in the way it treats people".

'Man of great peace'

Volunteer Mr Henning, 47, was on his fourth aid mission to Syria when he was captured within minutes of arriving in the country last December.

The prime minister said: "Alan Henning was a man of great peace, kindness and gentleness.

"He went with many Muslim friends out to do no more than simply help other people.

"His Muslim friends will be mourning him at this special time of Eid and the whole country is mourning with them."

The prime minister met ministers and officials at Chequers on Saturday

Mr Henning's wife had this week appealed for her husband's release, saying: "He is innocent."

She asked for "mercy", saying the family was still trying to communicate with her husband's captors. Mr Henning's family had earlier received an audio message of him pleading for his life.

Deputy Prime Minister Nick Clegg said Mr Henning was trying to help Muslims and had been "brutally murdered by an organisation that's twisting that religion to its own end".

His message to IS, also known as Isil or Isis, was: "If you are doing this to intimidate us, you won't. If you are doing this to break our resolve, you won't.

"If you are doing this to drag us into a religious war on your terms, you won't.

"What we in Britain will do instead in a calm and determined way is to play our role to hunt you down and to rid the world of this barbaric violence."

Analysis

Frank Gardner, security correspondent

David Cameron's vow to catch the jihadist killers of Alan Henning and bring them to justice would seem to match the mood of the nation.

But judging by the track record of previous such cases of hostages being murdered overseas, this promise has little likelihood of being fulfilled.

Tony Blair made the same pledge after Ken Bigley from Liverpool was beheaded in 2004, Gordon Brown did the same when tourist Edwin Dwyer was kidnapped and killed in the Sahara, and Mr Cameron vowed to punish those who besieged the Algerian gas plant last year.

According to the Crown Prosecution Service, there has not been one single case of any murderers of British hostages ever being brought to justice in Britain.